Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26020000 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 5. C89×#1295 | C2 | semidirect |
| 17. #19151337 | C4 | semidirect |
| 39. #15667923 | C2×C4 | semidirect |
| 46. #97×C89 | C2×C4 | semidirect |
| 154. #1295 | D89 | semidirect |
| 155. C89 | #8224 | semidirect |
| 195. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022791 | 2 |
| #26020000 | 2 |
| C2×#19151337 | 2 |
| #26018133 | 2 |
| C89×#1295 | 2 |
| #8224 | 89 |